Modeling turbulent flows in round pipes

A rheological model of a biviscous fluid is proposed, describing laminar and turbulent flows of Newtonian and non-Newtonian fluids in round cylindrical pipes. For low shear rates, common rheological models (Newton, Bingham, Ostwald, Herschel – Bulkley, Shulman – Casson, etc.) are used, and for high rates, a generalization of the L. Prandtl model is used. Taking into account the averaged flow characteristics, a model of turbulent flow and velocity distribution equations in round pipes are constructed. The model ensures the continuity of the dependence of hydraulic resistance on the fluid flow rate and expands the possibilities of its application in applied problems of hydromechanics. It is proposed to use capillary viscometry data for laminar and turbulent flow to provide information support for the rheological model. Using the principle of maximum likelihood function, the procedure for processing viscometry data for estimating the parameters of the biviscous rheological model is considered. Using the example of Herschel – Bulkley and Shulman – Casson fluids, the characteristics of flows in laminar and turbulent flow are given. Using known empirical formulas for determining the coefficient of hydraulic resistance in turbulent flow of Newton, Bingham, Ostwald, Herschel-Bulkley fluids, the possibility of using the proposed model is assessed. A comparison of the coefficient of hydraulic resistance using numerical 3D modeling and the equation of the biviscous model in turbulent flow of Ostwald fluid is given. Keywords: bi-viscous fluid; round pipes; calculation of hydraulic resistance; rheological model; turbulent flow.